Question 1: Use the identity 1+2+3++n= n(n+1)/2 to prove that 13+23+33 ++n³ = (1+2+3+...+n)². Question 2: Let S = {1,2,3,..., 9}, and let (a, b) (c, d) whenever a + d = b+c. (a) Prove that is an equivalence relation. - be the relation on A × A defined by (b) Find [(2,5)], that is, the equivalence class of (2,5).
Question 1: Use the identity 1+2+3++n= n(n+1)/2 to prove that 13+23+33 ++n³ = (1+2+3+...+n)². Question 2: Let S = {1,2,3,..., 9}, and let (a, b) (c, d) whenever a + d = b+c. (a) Prove that is an equivalence relation. - be the relation on A × A defined by (b) Find [(2,5)], that is, the equivalence class of (2,5).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Question 1: Use the identity 1+2+3++n= n(n+1)/2 to prove that
13+23+33 ++n³ = (1+2+3+...+n)².
Question 2: Let S = {1,2,3,..., 9}, and let
(a, b) (c, d) whenever a + d = b+c.
(a) Prove that is an equivalence relation.
-
be the relation on A × A defined by
(b) Find [(2,5)], that is, the equivalence class of (2,5).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa53d95c6-c6a4-4f40-9ff0-074a80b92257%2F0f918f34-dddd-4126-a306-ef7236a0ea15%2Fse7rwvb_processed.png&w=3840&q=75)
Transcribed Image Text:Question 1: Use the identity 1+2+3++n= n(n+1)/2 to prove that
13+23+33 ++n³ = (1+2+3+...+n)².
Question 2: Let S = {1,2,3,..., 9}, and let
(a, b) (c, d) whenever a + d = b+c.
(a) Prove that is an equivalence relation.
-
be the relation on A × A defined by
(b) Find [(2,5)], that is, the equivalence class of (2,5).
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